Saturation physics and the J/psi productions of CNM in p(d)-A collisions

1. Saturation physics and the J/psi productions of CNM in p(d)-A collisions 冯笙琴 三峡大学 fengsq@ctgu.edu.cn 第九届中国高能物理年会-武汉（华中师大）

2. Topics TOPICS • CGC and saturation physics • The J/psi productions of CNM in p(d)-A collisions • The results and discussions 第九届中国高能物理年会-武汉（华中师大）

3. 1. CGC and saturation physics 第九届中国高能物理年会-武汉（华中师大）

4. HERA Data pQCD ok ! HERA DATA Small x problem McLerran, NPA750(05)30 第九届中国高能物理年会-武汉（华中师大）

5. Valence partons as static random color source Small x gluons as radiation field created by r(x). Stochastic Yang-Mills equation 第九届中国高能物理年会-武汉（华中师大）

6. M.Gyulassy , L. D. McLerran， New forms of QCD matter discovered at RHIC，Nucl.Phys. A750 (2005) 30-63 Color Glass Condensate Hadronic interactions at very high energies are controlled by a new form of matter, a dense condensate of gluon. Color: Gluon are colored Glass: The gluons at small x are generated from gluons at larger values of x. The fields evolve very slowly with respect to the natural time scale and are disordered. Condensate: There is a very high density of mass-less gluons. These gluons can be packed until their phase space density is so high that interactions prevent more gluon occupation. 第九届中国高能物理年会-武汉（华中师大）

7. The two incoming nuclei look as two Lorentz–contracted ‘pancakes’, with alongitudinal extent smaller by a factor 100 (the Lorentz boost factor) than the radial extent inthe transverse plane. Heavy ion collisions at ultra-relativistic energies are visualized as the collision of two sheets of colored glass. The nuclei appear as sheets at ultra-relativistic energies because of Lorentz contraction. The CGC gluons are shown as vectors which represent the polarization of the gluons, and by colors corresponding to the various colors of gluons. 第九届中国高能物理年会-武汉（华中师大）

8. Multi-particle production in a hadronic collision Leading particles (projectile or target ) are shown in real line and are clustered around the projectile and target rapidity. In the dashed line, the distribution of produced mesons is shown. Note that y = 0 corresponds to particles with pz = 0 or for which is small, x ≪ 1, in the high-energy limit of interest. Thus the multiparticle production at central rapidity reflects properties of the small-x degrees of freedom in the colliding hadron wavefunctions. 第九届中国高能物理年会-武汉（华中师大）

9. There is a remarkable feature of rapidity distributions of produced hadrons, generally referred to as either Feynman scaling or Limiting fragmentation. If we plot rapidity distributions of produced hadrons at different energies, then as function of y−yproj The rapidity distributions are to a good approximation independent of energy. This is illustrated in right figure, where the rapidity distribution measured at lower energy is shown with a solid line and the rapidity distribution at a different and higher energy is shown with a dotted line. 第九届中国高能物理年会-武汉（华中师大）

10. This means that as we go to higher and higher energies, the new physics is associated with the additional degrees of freedom at small rapidity in the center of mass frame (small-x degrees of freedom). We shall see that in fact these large x degrees of freedom act as sources for the small x degrees of freedom. 第九届中国高能物理年会-武汉（华中师大）

11. Some scaling in p-A interactions Nucl.Phys. A774 (2006) 287 第九届中国高能物理年会-武汉（华中师大）

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13. Z. F. Jiang, S. Q. Feng, Y. F. Shi, Submitted to PRC 2. The J/psi productions of CNM in p(d)-A collisions 第九届中国高能物理年会-武汉（华中师大）

14. 胶子饱和构架下的p(d)-A碰撞的J/psi产生 高能碰撞下，此时将一个质子看成一团胶子与核发生碰撞，此时与核子发生碰撞的主要是胶子。 (1) In order to set normalization for , it is convenient to compare the gA scattering process in (1) with that of γA where there is a well developed phenomenology. State with γ-proton scattering where 胶子饱和特征质子-核作用 (2) 第九届中国高能物理年会-武汉（华中师大）

15. (3) The S factors are given, in the Mclerran-Venugopalan model, by (4) Here Qs is the gluon saturation momentum. The main change of necessary to convert (3) to a cross section forgA→J/Ψis the way the dipole scatters off nucleus. 第九届中国高能物理年会-武汉（华中师大）

16. F.Dominguez, D.Kharzeev, E.Levin, A.Mueller,K.Tuchin, PLB710,182-187(2012) Z. F. Jiang, S. Q. Feng, Y. F. Shi, Submitted to PRC 在g-A作用的色共轭表象中， 对来自于胶子， 对形成J/Ψ，对应为一个色单态， 对是通过偶极子-核子的非弹性碰撞而形成色单态的。这非弹性碰撞的点对应纵向坐标为 ，在 位置前，假设偶极子-核子碰撞都是弹性碰撞的，非弹碰撞后，维持色单态不变。见下图。 第九届中国高能物理年会-武汉（华中师大）

17. The interaction at , responsible of the transition from a color octet state to a color singlet state. Under the MV model evaluation employed here, the interactions probability of occurring before 第九届中国高能物理年会-武汉（华中师大）

18. Here T(b) is the nuclear profile function. Each of these pieces can be treated as a dipole interaction with the nucleus with dipole separation . This gives the combined factor: where the factor accounts for these interactions being present only the last inelastic interaction at longitudinal coordinate . 第九届中国高能物理年会-武汉（华中师大）

19. Interactions occurring after the last inelastic interactions preserve the singlet state of the quark-anti-quark system, this gives the combined factor where the factor accounts for these interactions being present only after the last inelastic interaction at longitudinal coordinate , that has to be included to account for the effective length where this kind of Interaction takes place. 第九届中国高能物理年会-武汉（华中师大）

20. 核厚度函数： d-A碰撞参量： 引入核相干作用项： 第九届中国高能物理年会-武汉（华中师大）

21. 对于夸克偶极子-核碰撞的向前弹性散射振幅：对于夸克偶极子-核碰撞的向前弹性散射振幅： Where subscript F indicates the fundamental representation. Evolution of the gluon dipole scattering amplitude (adjoint representation) obeys the equation: And its initial condition is The relation between them: 第九届中国高能物理年会-武汉（华中师大）

22. DHJ model We performed numerical calculations of dipole scattering amplitude by using DHJ models. The DHJ model takes into account the change in the anomalous dimension of the gluon distribution function due to the presence of the saturation boundary and takes into account the higher order effect. It successfully describes the single inclusive hadron production in d-A collisions. The dipole scattering amplitude is parameterized as follows: 第九届中国高能物理年会-武汉（华中师大）

23. The gluon saturation scale is given by: and 第九届中国高能物理年会-武汉（华中师大）

24. 胶子分布函数为： 根据M-V模型及DHJ模型，可以得到偶极子与靶核相互 作用的截面表达式为： 第九届中国高能物理年会-武汉（华中师大）

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26. Z. F. Jiang, S. Q. Feng, Y. F. Shi, Submitted to PRC 3. The results and discussions 第九届中国高能物理年会-武汉（华中师大）

27. F.Dominguez, D.Kharzeev, E.Levin, A.Mueller,K.Tuchin, PLB710,182-187(2012) Z. F. Jiang, S. Q. Feng, Y. F. Shi, Submitted to PRC The nuclear modification factor: 第九届中国高能物理年会-武汉（华中师大）

28. F.Dominguez, D.Kharzeev, E.Levin, A.Mueller,K.Tuchin, PLB710,182-187(2012) 中心度：0-100% 中心度：0-20% 中心度：60-88% Z. F. Jiang, S. Q. Feng, Y. F. Shi, Submitted to PRC 第九届中国高能物理年会-武汉（华中师大）

29. 用胶子饱和偶极子-核作用机制，讨论了冷核对J/psi产生的影响。给出的RdA-Npart在不同快度区间的关系, 可以解释实验结果。 • 同时也讨论了J/psi的 RdA- y 在不同中心度的关系。 第九届中国高能物理年会-武汉（华中师大）

30. Thanks 第九届中国高能物理年会-武汉（华中师大）